Accelerated Inchworm Method with Tensor-Train Bath Influence Functional

• URL: http://arxiv.org/abs/2506.12410v1
• Date: Sat, 14 Jun 2025 09:05:42 GMT
• Title: Accelerated Inchworm Method with Tensor-Train Bath Influence Functional
• Authors: Geshuo Wang, Yixiao Sun, Siyao Yang, Zhenning Cai,
• Abstract summary: We propose an efficient algorithm for simulating open quantum systems with the inchworm method.<n>We approximate the costly bath influence functional (BIF) in the integrand as a tensor train.<n>Thanks to the low-rank structure of the tensor train, our proposed method has a complexity that scales linearly with the number of dimensions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose an efficient tensor-train-based algorithm for simulating open quantum systems with the inchworm method, where the reduced dynamics of the open quantum system is expressed as a perturbative series of high-dimensional integrals. Instead of evaluating the integrals with Monte Carlo methods, we approximate the costly bath influence functional (BIF) in the integrand as a tensor train, allowing accurate deterministic numerical quadrature schemes implemented in an iterative manner. Thanks to the low-rank structure of the tensor train, our proposed method has a complexity that scales linearly with the number of dimensions. Our method couples seamlessly with the tensor transfer method, allowing long-time simulations of the dynamics.

Related papers

• Unraveling Open Quantum Dynamics with Time-Dependent Variational Monte Carlo [0.0]
  We introduce a method to simulate open quantum many-body dynamics by combining time-dependent variational Monte Carlo (VMC) with quantum trajectory techniques.<n>Our approach unravels the Lindblad master equation into an ensemble of Schr"odinger equations for a variational ansatz.<n>This work enables large-scale simulations of complex, dissipative quantum systems in higher dimensions, with broad implications for quantum technology and fundamental science.
  arXiv  Detail & Related papers  (2025-06-30T14:56:01Z)
• The Integral Decimation Method for Quantum Dynamics and Statistical Mechanics [44.99833362998488]
  We present a method to numerically evaluate functional integrals called integral decimation (ID)<n>ID enables high-accuracy simulations of quantum dynamics in systems as large as a 40-site chain.
  arXiv  Detail & Related papers  (2025-06-12T22:26:12Z)
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment. We find sufficient conditions under which dynamical decoupling works for such systems. Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Simulation of Spin Chains with off-diagonal Coupling Using Inchworm Method [0.0]
  We study the dynamical simulation of open quantum spin chain with nearest neighboring coupling, where each spin in the chain is associated with a harmonic bath. To reduce computational and memory cost in long time simulation, we apply tensor-train representation to efficiently represent the reduced density matrix of the spin chains.
  arXiv  Detail & Related papers  (2024-07-05T09:07:39Z)
• Adaptive Federated Learning Over the Air [108.62635460744109]
  We propose a federated version of adaptive gradient methods, particularly AdaGrad and Adam, within the framework of over-the-air model training. Our analysis shows that the AdaGrad-based training algorithm converges to a stationary point at the rate of $mathcalO( ln(T) / T 1 - frac1alpha ).
  arXiv  Detail & Related papers  (2024-03-11T09:10:37Z)
• Real-Time Simulation of Open Quantum Spin Chains with Inchworm Method [0.0]
  We study the real-time simulation of open quantum systems, where the system is modeled by a spin chain, with each spin associated with its own harmonic bath. Our method couples the inchworm method for the spin-boson model and the modular path integral methodology for spin systems.
  arXiv  Detail & Related papers  (2023-07-08T07:46:39Z)
• Deep Stochastic Mechanics [17.598067133568062]
  This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schr"odinger equation. Our method allows us to adapt to the latent low-dimensional structure of the wave function by sampling from the Markovian diffusion.
  arXiv  Detail & Related papers  (2023-05-31T09:28:03Z)
• D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory [79.50644650795012]
  We propose a deep learning approach to solve Kohn-Sham Density Functional Theory (KS-DFT) We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity. In addition, we show that our approach enables us to explore more complex neural-based wave functions.
  arXiv  Detail & Related papers  (2023-03-01T10:38:10Z)
• Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics [96.9177297872723]
  We present a novel method for guaranteeing linear momentum in learned physics simulations. We enforce conservation of momentum with a hard constraint, which we realize via antisymmetrical continuous convolutional layers. In combination, the proposed method allows us to increase the physical accuracy of the learned simulator substantially.
  arXiv  Detail & Related papers  (2022-10-12T09:12:59Z)
• Transfer-matrix summation of path integrals for transport through nanostructures [62.997667081978825]
  We develop a transfer-matrix method to describe the nonequilibrium properties of interacting quantum-dot systems. The method is referred to as "transfer-matrix summation of path integrals" (TraSPI)
  arXiv  Detail & Related papers  (2022-08-16T09:13:19Z)
• A quantum inspired approach to learning dynamical laws from data---block-sparsity and gauge-mediated weight sharing [0.0]
  We propose a scalable and numerically robust method for recovering dynamical laws of complex systems. We use block-sparse tensor train representations of dynamical laws, inspired by similar approaches in quantum many-body systems. We demonstrate the performance of the method numerically on three one-dimensional systems.
  arXiv  Detail & Related papers  (2022-08-02T17:00:26Z)
• Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion [68.8204255655161]
  We present a methodology for simulating multi-dimensional electronic spectra of molecular aggregates with coupling electronic excitation to a structured environment. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space but with the same noise.
  arXiv  Detail & Related papers  (2022-07-06T15:30:38Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell [0.0]
  tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems. We generalize a recently proposed variational uniform matrix product state algorithm for capturing one-dimensional quantum lattices. A key property of the algorithm is a computational effort that scales linearly rather than exponentially in the size of the unit cell.
  arXiv  Detail & Related papers  (2020-03-02T19:01:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.